1500 customers hold a VISA card; 500 hold an American Express card; and, 75 hold a VISA and an American Express. What is the probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card?

There is 15% probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.

Step-by-step explanation:

Number of customers having a Visa card = 1,500

Number of customers having an American Express card = 500

Number of customers having Visa and American Express card = 75

Total number of customers = 1,500 + 500 = 2,000

We are asked to find the probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.

This problem is related to conditional probability which is given by

For the given problem it becomes

The probability P(VISA and AE) is given by

P(VISA and AE) = 75/2000

P(VISA and AE) = 0.0375

The probability P(AE) is given by

P(AE) = 500/2000

P(AE) = 0.25

Finally,

Therefore, there is 15% probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.

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